As a hub museum, the Harris received about £500,000 a year from the Museums, Libraries and Archive Council.
But without a designated collection the museum was ineligible for major grant funding, although it did receive £229,000 in transitional funding from the Arts Council England (ACE) – including £57,000 ringfenced for redundancies.
The 10 affected staff come from across the organisation, including part and full-time learning, collections care, exhibitions and marketing posts.
Alex Walker, head of arts and heritage at Preston City Council, said: “We recognise that museums cannot be immune to the effects of the financial downturn. However I am very sorry that we will be losing valued and talented members of the workforce, from this museum and the others across the country which are losing posts.
“In the current climate some will find it difficult to find jobs and their knowledge and experience will be lost to the sector.”
Affected staff are expected to leave following the completion of the new £1.3m Discover Preston gallery, which opens in August, and the Preston Guild celebrations in early September.
Opening hours will not be affected by the restructure and although the museum will reduce temporary exhibitions, Walker said it remains committed to an “ambitious” contemporary art programme.
A new post has been created to develop an activity programme for the new gallery and the transitional funding has helped to establish a fundraising team.
Walker said the Harris will also apply to the Renaissance strategic fund later this year for funding from April 2013.
“Preston City Council is also working closely with Lancashire County Council and the University of Central Lancashire to develop a shared vision for arts and culture in Preston,” she added.